Bayesian analyses of the role of conscious influence of the prime in the AMP effect

Using posteriors as priors

Experiment 1

Weak, non-informative prior

Fit model

Posterior checks

Results

NB Not a box plot: outer error bars are 95% HDI, inner error bars are 50% HDI.

			95% CI
Parameter	Std. Beta	SE	Lower	Upper	% inside ROPE	Eff.Sample	Rhat
Intercept	0.17	0.02	0.12	0.21	0.45	3209.36	1
influence_rate	0.37	0.05	0.26	0.47	0.00	3094.83	1

Bayes factors

Savage-Dickey Bayes Factor (BF10) = 253889245582274112.

Posterior evidence ratio (Bayesian p value) = 0.

Experiment 2

Weak, non-informative prior

Fit model

Posterior checks

Results

NB Not a box plot: outer error bars are 95% HDI, inner error bars are 50% HDI.

			95% CI
Parameter	Std. Beta	SE	Lower	Upper	% inside ROPE	Eff.Sample	Rhat
Intercept	0.19	0.03	0.13	0.25	0.18	2903.35	1
influence_rate	0.41	0.05	0.31	0.52	0.00	3505.53	1

Bayes factors

Savage-Dickey Bayes Factor (BF10) = 46383622024772182016.

Posterior evidence ratio (Bayesian p value) = 0.

Informed prior

Posterior of exp 1 as prior for exp 2

Parameterise the posterior distributions of the previous model (intercept, slope of influence rate, and its sigma) as normal distributions, use their M and SD as the prior for this model.

##        mean         sd
## 1 0.3674058 0.05471254

Fit model

Posterior checks

Results

NB Not a box plot: outer error bars are 95% HDI, inner error bars are 50% HDI.

			95% CI
Parameter	Std. Beta	SE	Lower	Upper	% inside ROPE	Eff.Sample	Rhat
Intercept	0.12	0.02	0.07	0.16	19.43	3377.22	1
influence_rate	0.39	0.04	0.32	0.46	0.00	3641.59	1

Bayes factors

Savage-Dickey Bayes Factor (BF10) = -0.018.

Posterior evidence ratio (Bayesian p value) = 0.

Experiment 3

Weak, non-informative prior

Fit model

Posterior checks

Results

NB Not a box plot: outer error bars are 95% HDI, inner error bars are 50% HDI.

			95% CI
Parameter	Std. Beta	SE	Lower	Upper	% inside ROPE	Eff.Sample	Rhat
Intercept	0.10	0.02	0.06	0.14	47.62	2974.45	1
influence_rate	0.59	0.04	0.51	0.68	0.00	2691.31	1

Bayes factors

Savage-Dickey Bayes Factor (BF10) = 1702613387701247232.

Posterior evidence ratio (Bayesian p value) = 1702613387701247232.

Informed prior

Posterior of exp 2 as prior for exp 3

Parameterise the posterior distributions of the previous model (intercept, slope of influence rate, and its sigma) as normal distributions, use their M and SD as the prior for this model.

##        mean         sd
## 1 0.3893986 0.03737608

Fit model

Posterior checks

Results

NB Not a box plot: outer error bars are 95% HDI, inner error bars are 50% HDI.

			95% CI
Parameter	Std. Beta	SE	Lower	Upper	% inside ROPE	Eff.Sample	Rhat
Intercept	0.07	0.02	0.03	0.10	98.33	3741.77	1
influence_rate	0.45	0.03	0.39	0.51	0.00	3512.80	1

Bayes factors

Savage-Dickey Bayes Factor (BF10) (with mu = 0) = 0.

Posterior evidence ratio (Bayesian p value) = 0.

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1. Ghent University. Email: ian.hussey@ugent.be↩